Propagation of Twist Solitons in Fully Inhomogeneous DNA Chains

Abstract

In the framework of a recently introduced model of DNA torsional dynamics, we argued -on the basis of perturbative considerations -that an inhomogeneous DNA chain could support long-lived soliton-type excitations due to the peculiar geometric structure of DNA and the effect of this on nonlinear torsional dynamics. Here we consider an inhomogeneous version of this model of DNA torsional dynamics, and investigate numerically the propagation of solitons in a DNA chain with a real base sequence (corresponding to the Human Adenovirus 2); this implies inhomogeneities of up to 50% in the base masses and inter-pair interactions. We find that twist solitons propagate for considerable distances (2-10 times their diameters) before stopping due to phonon emission. Our results show that twist solitons may exist in realistic DNA chain models, and on a more general level that solitonic propagation can take place in highly inhomogeneous media. The most relevant feature for general nonlinear dynamics is that we identify the physical mechanisms allowing this behavior and thus the class of models candidate to support long-lived soliton-type excitations in the presence of significant inhomogeneities.

Speed selection for coupled wave equations

“…To solve the general linear case we well make use of the linear character of the field equations (6), and pass to consider the Fourier transforms f (q, ω) and g(q, ω) for, respectively, the fields ϕ(x, t) and ψ(x, t); the equations (6) are then recast as…”

“…When the full model, including the interaction, is considered, there is no Lorentz invariance, and the travelling wave solutions admits only a given speed (see also [4]). Thus we have a selection mechanism for the speed of travelling wave (TW) solutions (the latter turn out to be also stable and thus physically relevant [3,4,5,6,7]).…”

A review on nonlinear DNA physics

“…7: 200774 topological and non-topological degrees of freedom, respectively [11]. This approach can be further extended describing inhomogeneous DNA chains [12].…”

Ensemble of DNA Kinks

“…υ , (12) and the statistical sum (or partition function) Z [19] and the Gibbs distribution ρ(P,Q) [20] take the form:…”

“…To describe the open states mathematically, the instrument of theoretical physics and nonlinear mathematics are often used including representations about kinks, antikinks, and breathers. In this paper, following the work of Englander and coauthors [1] as well as the works of their followers [8][9][10][11][12][13], we shall use the sine-Gordon equation to model the internal dynamics of DNA, and shall apply the one-soliton solutions of the sine-Gordon equation -kinks, to describe the DNA open states.…”